Preheat oven to 400 degrees F.
In a large bowl, beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, cinnamon, baking powder, the ground nutmeg, the ginger, salt, and cloves. Beat until combined, scraping side of bowl occasionally. Beat in pumpkin, egg, and vanilla until combined. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour.
Place dough in a pastry bag fitted with a large open tip. Pipe dough, using a corkscrew motion, onto an ungreased cookie sheet into 4-inch-long strips.
Bake in the preheated oven for 5 to 7 minutes or just until firm to the touch but not browned. Cool on cookie sheet for 1 minute. Transfer cookies to a wire rack; let cool.
Drizzle Cream Cheese Glaze over half of each cookie. If desired, sprinkle with grated nutmeg. Let stand about 2 hours or until glaze is set. Makes about 30 cookies.
CREAM CHEESE GLAZE:
In a medium bowl, combine half of a 3-ounce package softened cream cheese and 1 tablespoon softened butter. Beat with an electric mixer on medium speed until smooth. Add 1/4 teaspoon finely shredded lemon peel, 1 teaspoon lemon juice, and 1/4 teaspoon finely shredded orange peel; beat until combined. Beat in 3/4 cup powdered sugar. Beat in enough milk (2 to 3 teaspoons) to make a glaze of drizzling consistency.
Layer cookies between waxed paper in an airtight container; cover. Store at room temperature for up to 3 days or freeze for up to 3 months.